Hiroshima Mathematical Journal

Discrete initial value problems and discrete parabolic potential theory

Fumi-Yuki Maeda, Atsushi Murakami, and Maretsugu Yamasaki

Full-text: Open access

Article information

Source
Hiroshima Math. J., Volume 21, Number 2 (1991), 285-299.

Dates
First available in Project Euclid: 21 March 2008

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1206128812

Digital Object Identifier
doi:10.32917/hmj/1206128812

Mathematical Reviews number (MathSciNet)
MR1098819

Zentralblatt MATH identifier
0734.31009

Subjects
Primary: 39A12: Discrete version of topics in analysis
Secondary: 31B35: Connections with differential equations 31C20: Discrete potential theory and numerical methods

Citation

Maeda, Fumi-Yuki; Murakami, Atsushi; Yamasaki, Maretsugu. Discrete initial value problems and discrete parabolic potential theory. Hiroshima Math. J. 21 (1991), no. 2, 285--299. doi:10.32917/hmj/1206128812. https://projecteuclid.org/euclid.hmj/1206128812


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References

  • [1] J. L. Doob, Classical potential theory and its probabilistic counterpart, Springer-Verlag, New York etc., 1983.
  • [2] F-Y. Maeda, Dirichlet integrals on harmonic spaces, Lecture Notes Math. 803, Springer-Verlag, Berlin etc.,1980.
  • [3] F-Y.Maeda, Dirichlet integral and energy of potentials on harmonic spaces with adjoint structure, Hiroshima Math. J. 18 (1988), 1-14.
  • [4] N. A. Watson, Green functions, potentials, and the Dirichlet problem for the heat equation, Pore. London Math. Soc. 33 (1976), 251-298.
  • [5] M. Yamasaki, Parabolic and hyperbolic infinite networks, Hiroshima Math. J. 7 (1977), 135-146.
  • [6] M. Yamasaki, Discrete potentials on an infinite network, Mem. Fac. Sci. Shimane Univ. 13 (1979), 31-44.
  • [7] M. Yamasaki, The equation Au = qu on an infinite network, Mem. Fac. Sci. Shimane Univ. 21 (1987), 31-46.